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Multi-step algorithms for solving equilibrium problems

    Pham Ngoc Anh Affiliation
    ; Dang Van Hieu Affiliation

Abstract

The paper introduces and analysizes the convergence of two multi-step proximal-like algorithms for pseudomonotone and Lipschitz-type continuous equilibrium problems in a real Hilbert space. The algorithms are combinations between the multi-step proximal-like method and Mann or Halpern iterations. The weakly and strongly convergent theorems are established with the prior knowledge of two Lipschitz-type continuous constants. Moreover, by choosing two sequences of suitable stepsizes, we also show that the multi-step proximal-like algorithm for strongly pseudomonotone and Lipschitz-type continuous equilibrium problems where the construction of solution approximations and the establishing of its convergence do not require the prior knowledge of strongly pseudomonotone and Lipschitz-type continuous constants of bifunctions. Finally, several numerical examples are reported to illustrate the convergence and the performance of the proposed algorithms over classical extragradient-like algorithms.

Keyword : proximal-like method, extragradient method, equilibrium problem, multi-step method, Lipschitz-type continuous

How to Cite
Anh, P., & Hieu, D. (2018). Multi-step algorithms for solving equilibrium problems. Mathematical Modelling and Analysis, 23(3), 453-472. https://doi.org/10.3846/mma.2018.027
Published in Issue
Jul 4, 2018
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This work is licensed under a Creative Commons Attribution 4.0 International License.

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